The drone strikes Saturday on national energy giant Aramco's processing plants in Abqaiq and Khurais knocked 5.7 million barrels per day (bpd) off production, close to six per cent of global crude supplies.
"Part of the drop will be compensated to clients" from storage facilities, new energy minister Prince Abdulaziz bin Salman said in a statement on the official SPA news agency.
The disruption represents half the output of the kingdom, which is the world's biggest oil supplier.
Riyadh has built five giant underground storage facilities in various parts of the country that can hold tens of millions of barrels of various refined petroleum products, to be tapped during times of crisis.
The facilities were constructed between 1988 and 2009 and cost tens of billions of dollars.
Prince Abdulaziz said Saturday's explosions also halted supplies of some two billion cubic feet of associated gas -- which is extracted along with the crude.
"As a result, ethane and LNG supplies will shrink by 50 percent," said the minister, adding that domestic supplies of fuel, electricity and water had not been affected.
As markets closely watch the OPEC kingpin's ability to get its industry back on track, Aramco CEO Amin Nasser said that "work is underway" to restore full production.
Abqaiq is the world's largest oil processing plant and can handle up to seven million bpd, some 70 percent of total Saudi output.
It is located near Ghawar oilfield, the biggest in the world with reserves of over 60 billion barrels and a daily output capacity of six million bpd.
The plant also receives crude oil and gas from Shayba oilfield in the Empty Quarter.
Yemen's Iran-aligned Huthi rebels have claimed responsibility for the attack but US Secretary of State Mike Pompeo blamed Tehran, saying there was no evidence it was launched from Yemen.
"Iran has now launched an unprecedented attack on the world's energy supply," Pompeo said.
Last month, an attack also claimed by Huthi rebels sparked a fire at Aramco's Shaybah natural gas liquefaction facility, close to the Emirati border, with no casualties reported.
The Huthis also claimed a May drone attack on two oil pumping stations on Saudi Arabia's key east-west pipeline, which caused a days-long shutdown.
